A parallel plate capacitor consisting of two circular plates of radius $10\ \text{cm}$ is being charged by a constant current of $0.15\ \text{A}$. If the rate of change of potential difference between the plates is $7\times10^8\ \text{V/s}$, then the integer value of the distance between the parallel plates is ______ $\mu$m. (Take $\epsilon_0 = 9\times10^{-12}\ \text{F/m}$, $\pi = \dfrac{22}{7}$)
Numerical value type. Enter your answer.
Answer: 1320
$I = C\dfrac{dV}{dt} \Rightarrow C = \dfrac{0.15}{7\times10^8} = \dfrac{3}{14}\times10^{-9}\ \text{F}$.
$C = \dfrac{\epsilon_0\pi r^2}{d}$:
$$d = \frac{\epsilon_0\pi r^2}{C} = \frac{9\times10^{-12}\times\frac{22}{7}\times10^{-2}}{\frac{3}{14}\times10^{-9}} = \frac{9\times22\times14}{7\times3}\times10^{-5} = 132\times10^{-5}\ \text{m} = 1320\ \mu\text{m}$$
Solution by Sreeraj P, M.Sc Physics